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This mock test of VITEEE PCME Mock Test - 8 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 8 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

For the curve x = t^{2} - 1, y = t^{2 }- t tangent is parallel to x-axis where

Solution:

QUESTION: 2

The area, in square unit, bounded by the curves * y = x ^{3}, y = x^{2}* and the ordinates

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QUESTION: 3

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QUESTION: 4

If z and ω are two non-zero complex numbers such that |z ω | = 1, and arg(z) - arg(ω)= π/2,then z̅ω is equal to

Solution:

QUESTION: 5

Solution:

QUESTION: 6

The derivative of an odd function is an

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QUESTION: 7

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QUESTION: 8

Suppose ω is an imaginary cube root of unity. If (1+ω^{2})^{m} = (1+ω^{4})^{m}, then the least positive integral value of m is

Solution:

The given equation reduces to (−ω)^{m} = (−ω^{2})^{m}

⇒ ω^{m} = 1

⇒ m = 3

QUESTION: 9

is continuous at *x* = 0, then *k* =

Solution:

QUESTION: 10

The differential equation which represents the family of plane curves y=exp. (cx) is

Solution:

y = e^{cx}

dy/dx = c. e^{cx}

y' = cy

QUESTION: 11

The differential equation representing the family of curves y^{2} = 2c(x + √c), where c>0, is a parameter, is of order and degree as follows

Solution:

QUESTION: 12

If y = y(x) and [(2 + sin x)∕(y + 1)(dy∕dx)] = -cos x, y(0) = 1, then y (π∕2) equals

Solution:

QUESTION: 13

If siny=x sin (a+y), (dy/dx)=

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QUESTION: 14

Integrating factor of

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QUESTION: 15

If f(x) = cos (logx), then f(x) f(y) -1/2[f(x/y) + f(xy)] has the value

Solution:

QUESTION: 16

∫sin√x dx =

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QUESTION: 17

∫[(sec^{2}x)/(1+tanx)] dx =

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QUESTION: 18

If sin (sin⁻^{1} 1/5 + cos^{-1} x) = 1, then x is equal to

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QUESTION: 19

If a , b , c , d are positive real numbers then

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QUESTION: 20

Solution:

QUESTION: 21

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

Solution:

Statements are logically equivalent to their contrapositives.

QUESTION: 22

If A is a singular matrix, then A adj (A)

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QUESTION: 23

If the value of a determinants is 11, then the square of the determinant formed by its cofactor will be

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QUESTION: 24

How many words can be formed from the letters of the word MATHEMATICS?

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QUESTION: 25

\'A\' draws two cards with replacement from a pack of 52 cards and \'B\' throws a pair of dice. What is the chance that \'A\' gets both cards of same suit and \'B\' gets total of 6?

Solution:

QUESTION: 26

The probabiltiy that the two digit number formed by digits 1,2,3,4 is divisible by 4, is

Solution:

QUESTION: 27

A single letter is selected at random from the word PROBABILITY. The probability that it is a vowel is

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QUESTION: 28

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QUESTION: 29

The fourth ,seventh and tenth of a G.P. are p,q,r respectively then

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QUESTION: 30

Which of the following measures of marks is the most suitable one of central location for computing intelligence of students?

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QUESTION: 31

A batsman scores runs in 10 innings 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44, then the mean deviation is

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QUESTION: 32

In equation 2^{|x+1|}-2^{x}=|2^{x}-1|+1 the values of x are

Solution:

QUESTION: 33

The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}-4x-6y-8z=0 and which passes thro' (0.1,0) is

Solution:

QUESTION: 34

If √2 + √3 + i be one of the roots of a given equation f(x) = 0 with real coefficients, then the lowest degree of such an equation must be____

Solution:

Since the complex and irrational roots occure in pairs, therefore, if one root is 2 + √3 + i , then the other roots are

QUESTION: 35

The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2} - 4x - 6y - 8z - 5 = 0 and which passes through the point (0, 1, 0) is

Solution:

QUESTION: 36

If m_{1}, m_{2} are slopes of the two tangents that are drawn from (2, 3) to the parabola y^{2} = 4x, then the value of [(1/m_{1}) + (1/m_{2})] is

Solution:

QUESTION: 37

If P is any point on the hyperbola [(x - 1)^{2}/9 - (y + 1)^{2}/16] = 1 and S_{1}, S_{2} are its foci, then | s_{1} P - S_{2} P |

Solution:

QUESTION: 38

The values of 'θ' satisfying sin 7θ = sin 4θ - sin θ in 0 < θ < π/2 are

Solution:

sin 7θ + sin θ - sin 4θ = 0

⇒ 2 sin 4θ . cos 3θ - sin 4θ = 0

⇒ sin 4θ [2 cos 3θ - 1] = 0

⇒ sin 4θ = 0 or cos 3θ = 1/2 = cos ( π/3 )

⇒ 4θ = nπ or 3θ = 2nπ ( π/3 )

⇒ θ = nπ/4 or θ = ( 2nπ/3 ) ( π/9 )

∴ The values of θ are π/4 , π/9

QUESTION: 39

The angle between the vectors i-j+k and i+2j+k is

Solution:

QUESTION: 40

The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=

Solution:

QUESTION: 41

In an A.C. circuit, the power factor

Solution:

QUESTION: 42

The value of de-Broglie wavelength of an electron moving with a speed of 6.6 x 10^{5} m s^{-1} is approximately [ h = 6.6 x 10^{-34} J − sec , mass of electron = 9 x 10^{-31} Kg ]

Solution:

QUESTION: 43

A photon of energy 2.5eV and wavelength λ falls on a metal surface and the ejected electrons have a velocity *'V'* . If the wave length λ of incident light is decreased by 20%, the velocity of emitted electrons is doubled, then the work function of the metal is

Solution:

QUESTION: 44

9 gm of silver is deposited in 20 min. by a battery of 24 V. How many gms will be deposited in 40 min. by a battery of 8 V?

Solution:

QUESTION: 45

If sky wave with a frequency of 50 MHz is incident on D-region at an angle of 30^{o}, then angle of refraction is

Solution:

QUESTION: 46

Minimum resistance of a circuit, with n resistance 'R' each combination is

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QUESTION: 47

If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21%. The original charge on the capacitor is

Solution:

QUESTION: 48

Which statement is true ?

(i) Kirchhoff's law is not equally applicable to both AC and DC.

(ii) Semiconductors have a positive temperature coefficient of resistance.

(iii) Meter bridge is least sensitive when the resistance of all the four arms of the bridge are of the same order .

(iv) The emf of a cell depends upon the size and area of electrodes.

(i) Kirchhoff's law is not equally applicable to both AC and DC.

(ii) Semiconductors have a positive temperature coefficient of resistance.

(iii) Meter bridge is least sensitive when the resistance of all the four arms of the bridge are of the same order .

(iv) The emf of a cell depends upon the size and area of electrodes.

Solution:

QUESTION: 49

A wire of length L is drawn such that its diameter is reduced to half of its original diameter. If the initial resistance of the wire were 10Ω, its new resistance would be

Solution:

We have kept the volume of the wire constant i.e.

QUESTION: 50

In an experiment to measure the internal resistance of a cell, by a potentiometer, it is found that the balance point is at a length of 2 m, when the cell is shunted by a 5 Î© resistance and is at a length of 3m when the cell is shunted by a 10 Î© resistance. The internal resistance of the cell is

Solution:

QUESTION: 51

If an electron and a photon propagates in the form of waves having the same wavelength, it implies that they have the same

Solution:

QUESTION: 52

A generator at a utility company produces 100 A of current at 4000 V. The voltage is stepped up to 240000 V by a transformer before it is sent on a high voltage transmission line. The current in transmission line is

Solution:

QUESTION: 53

The expression for magnetic induction inside a solenoid of length L, carrying a current I and having N number of turns is

Solution:

QUESTION: 54

Which of the following waves have maximum wavelength?

Solution:

QUESTION: 55

A charge is placed at the centre of a cube, the flux emitted through its one face is

Solution:

QUESTION: 56

A charge of 5 C is given a displacement of 0.5 m. The work done in the process is 10 J. The potential difference between the two points will be

Solution:

QUESTION: 57

Consider the situation shown in figure. Work done in carrying a point charge from *k* to *A, B, C* are ${W}_{A},{W}_{B},{W}_{C}$ respectively. Which one is true?

Solution:

QUESTION: 58

The ratio of charge to potential of a capacitor is known as its

Solution:

QUESTION: 59

Two point charges +8q and -2q are located at x = 0 and x = L respectively. The location of a point on the x-axis, at which the net electric field due to these two point charges is zero, is

Solution:

QUESTION: 60

To send 10% of the main current, through a moving coil galvanometer of resistance 99â„¦, the shunt required is

Solution:

QUESTION: 61

The inductance of a coil is L = 10 H and resistance R = 5 Ω . If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor.

Solution:

QUESTION: 62

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

Solution:

QUESTION: 63

The rest energy involved in a mass of one atomic mass unit is ---- eV.

Solution:

QUESTION: 64

Solution:

QUESTION: 65

Assuming photoemission to continue to take place, the factor by which the maximum velocity of the emitted photoelectrons changes when the wavelength of the incident radiation is increased four times, is

Solution:

QUESTION: 66

When the light source is kept 20 cm away from a photo cell, stopping potential 0.6 V is obtained. When source is kept 40 cm away, the stopping potential will be

Solution:

QUESTION: 67

A mirror produces magnified erect image of an object. The nature of the mirror is

Solution:

QUESTION: 68

The energy stored in a capacitor is actually stored

Solution:

QUESTION: 69

The distance travelled by light in glass (refractive index =1.5) in a nanosecond will be

Solution:

Speed of light in glass

Distance travelled in one nanosecond

= 2 x 10^{8} x 10^{-9} = 0.2 m = 20 cm

QUESTION: 70

The voltage gain of an amplifier with 9% negative feedback is 10. The voltage gain without feedback will be

Solution:

QUESTION: 71

To obtain *p* - type extrinsic semiconductor, the impurity element to be added to Germanium should be of valence

Solution:

QUESTION: 72

The dominant mechanism for motion of charge carriers in forward and reverse biased silicon p-n junction are

Solution:

QUESTION: 73

Electronic configuration of Germanium is 2, 8, 18 and 4. To make it extrinsic semiconductor small quantity of antimony is added

Solution:

QUESTION: 74

A rectifier converts

Solution:

QUESTION: 75

Electronic configuration of germanium is 2, 8, 18 and 4. To make it extrinsic semiconductor small quantity of antinomy is added

Solution:

QUESTION: 76

In the forward bias arrangement of a p-n junction diode

Solution:

QUESTION: 77

A wave front is the locus of all the particles of a medium, which are vibrating in the

Solution:

QUESTION: 78

The golden view of sea shell is due to

Solution:

QUESTION: 79

Two sources of same intensity interfere at a point and produced resultant *I*. When one source is removed, the intensity at that point will be

Solution:

QUESTION: 80

In Young's experiment of double slit, the intensity of central bright band is ---- times the individual intensities of the interfering waves

Solution:

QUESTION: 81

In presence of alkali, C₂H₅OH reacts with Cl₂ to give

Solution:

QUESTION: 82

At room temperature formaldehyde is

Solution:

QUESTION: 83

Schiff's reagent is

Solution:

QUESTION: 84

The product acetal is produced by reacting alcohol in the presence of dry HCl with

Solution:

QUESTION: 85

The addition of *HBr* to 2-pentene gives

Solution:

QUESTION: 86

The ratio of the molar amounts of H₂S needed to precipitate the metal ions from 20 mL each of 1M Cd(NO₃)₂ and 0.5 M CuSO₄ is

Solution:

As Cd^{2+} and Cu^{2+}, both are dipositive ions but Cu^{2+} has one half of the concentration compared to that of the Cd^{2+}. Thus, the molar amount of the H_{2}S used to precipitate the metals ions Cd^{2+} and Cu^{2+} is 2 : 1.

QUESTION: 87

How many monochlorobutanes will be obtained on chlorination of n-butane?

Solution:

QUESTION: 88

The unit for electric current is

Solution:

QUESTION: 89

Which one of the following compounds is not a vitamin?

Solution:

QUESTION: 90

The substances which act as emulsifiers in lipid metabolism are

Solution:

QUESTION: 91

Scurvy is caused due to the deficiency of vitamin

Solution:

QUESTION: 92

The following reaction is called

2 CH₃COOC₂H₅ → CH₃COCH₂COOC₂H₅

Solution:

QUESTION: 93

Which of the following is the strongest acid?

Solution:

QUESTION: 94

Vinegar made from cane sugar, now-a-days synthetically contains

Solution:

QUESTION: 95

The role of a catalyst in a reversible reaction is to

Solution:

QUESTION: 96

Calculate Δ H in KJ for the following reaction C(s)+ O_{2} g → CO_{2} g Given that

H_{2}O g + C g → CO g + H_{2} g , Δ H = + 131 k J

CO g + 1/2 O_{2} g → CO_{2} g , Δ H = − 282 k J

H_{2} g + 1/2 O_{2} g →H_{2}O g , Δ H = − 242 k J

Solution:

QUESTION: 97

The rate, at which a substance reacts at constant temperature, depends upon its

Solution:

QUESTION: 98

The free energy change ∆G=0, when

Solution:

QUESTION: 99

Which of the following ingredients is not used in sun burn creams?

Solution:

QUESTION: 100

Which of the following will show geometrical isomerism ?

Solution:

QUESTION: 101

Standard enthalpy and standard entropy changes for the oxidation of ammonia at 298 K are - 382.64 kJ mol^{-1} and - 145.6 JK^{-1} mol^{-1} respectively. The standard Gibbs energy change for the same reaction 298 K is

Solution:

QUESTION: 102

How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca^{2+} ion?

Solution:

QUESTION: 103

Acetaldoxime reacts with P₂O₅ to give

Solution:

QUESTION: 104

Which of the following compound gives dye test ?

Solution:

QUESTION: 105

A complex compound of Co^{2+} with molecular formula CoCl_{xy}NH₃ gives a total of three ions per molecule when dissolved in water. How many Cl⁻ ions satisfy primary as well secondary valencies in this complex?

Solution:

QUESTION: 106

The amount of electricity that can deposit 108 g of silver from silver nitrate solution is

Solution:

QUESTION: 107

Which of the following is a strong electrolyte?

Solution:

QUESTION: 108

The quantity of electricity required to liberate 112 cm^{3} of hydrogen at STP from acidified water is

Solution:

QUESTION: 109

The important oxide ore of iron is

Solution:

QUESTION: 110

Among the following oxides, the least acidic is

Solution:

QUESTION: 111

Use of hot air balloons in sports and metereological observations is an application of

Solution:

QUESTION: 112

When ether is exposed in air for sometime, an explosive substance produced is

Solution:

QUESTION: 113

An alloy which does not contain copper is

Solution:

QUESTION: 114

Nitrogen shows different oxidation states in the range

Solution:

QUESTION: 115

Solution:

QUESTION: 116

In CsCl structure, each Cs⁺ ion is surrounded by

Solution:

QUESTION: 117

Zn^{2+}aq) + 2e^{-} → Zn(s). This is

Solution:

QUESTION: 118

Cupric hydroxide dissolves in aqueous ammonia due to

Solution:

QUESTION: 119

The formation of a colloid from suspension is

Solution:

QUESTION: 120

Cuprous ion is colourless while cupric ion is coloured because

Solution:

QUESTION: 121

Find the antonym of DEROGATORY

Solution:

QUESTION: 122

Find the Synonym of BLADERDASH

Solution:

QUESTION: 123

Fill in the blank with appropriate word.

Many of the advances of civilisation have been conceived by young people just on the........of adulthood

Solution:

QUESTION: 124

**Out of the given alternatives, choose the one which can be substituted for the given capitalised word. **

The police fired AT RANDOM at the violent crowd and several persons lost their lives.

Solution:

QUESTION: 125

**Improve the sentence by choosing best alternative for capitalised part of the sentence.**

Last evening I went to the optician and bought SPECTACLES

Solution:

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